{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from datetime import datetime\n",
    "from datetime import timedelta\n",
    "from pandas.plotting import register_matplotlib_converters\n",
    "from statsmodels.tsa.stattools import acf, pacf\n",
    "from statsmodels.tsa.arima_model import ARMA\n",
    "register_matplotlib_converters()\n",
    "from time import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Catfish Sales Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def parser(s):\n",
    "    return datetime.strptime(s, '%Y-%m-%d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#read data\n",
    "catfish_sales = pd.read_csv('catfish.csv', parse_dates=[0], index_col=0, squeeze=True, date_parser=parser)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#infer the frequency of the data\n",
    "catfish_sales = catfish_sales.asfreq(pd.infer_freq(catfish_sales.index))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "start_date = datetime(2000,1,1)\n",
    "end_date = datetime(2004,1,1)\n",
    "lim_catfish_sales = catfish_sales[start_date:end_date]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1e8323fd408>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(lim_catfish_sales)\n",
    "plt.title('Catfish Sales in 1000s of Pounds', fontsize=20)\n",
    "plt.ylabel('Sales', fontsize=16)\n",
    "for year in range(start_date.year,end_date.year):\n",
    "    plt.axvline(pd.to_datetime(str(year)+'-01-01'), color='k', linestyle='--', alpha=0.2)\n",
    "plt.axhline(lim_catfish_sales.mean(), color='r', alpha=0.2, linestyle='--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_diff = lim_catfish_sales.diff()[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1e831e40888>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(first_diff)\n",
    "plt.title('First Difference of Catfish Sales', fontsize=20)\n",
    "plt.ylabel('Sales', fontsize=16)\n",
    "for year in range(start_date.year,end_date.year):\n",
    "    plt.axvline(pd.to_datetime(str(year)+'-01-01'), color='k', linestyle='--', alpha=0.2)\n",
    "plt.axhline(first_diff.mean(), color='r', alpha=0.2, linestyle='--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ACF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 20 artists>"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "acf_vals = acf(first_diff)\n",
    "plt.bar(range(num_lags), acf_vals[:num_lags])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Based on ACF, we should start with a MA(1) process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PACF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 15 artists>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pacf_vals = pacf(first_diff)\n",
    "plt.bar(range(num_lags), pacf_vals[:num_lags])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Based on PACF, we should start with a AR(4) process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Get training and testing sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_end = datetime(2003,7,1)\n",
    "test_end = datetime(2004,1,1)\n",
    "\n",
    "train_data = first_diff[:train_end]\n",
    "test_data = first_diff[train_end + timedelta(days=1):test_end]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit the ARMA Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define model\n",
    "model = ARMA(train_data, order=(4,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model Fitting Time: 0.6803164482116699\n"
     ]
    }
   ],
   "source": [
    "#fit the model\n",
    "start = time()\n",
    "model_fit = model.fit()\n",
    "end = time()\n",
    "print('Model Fitting Time:', end - start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:                  Total   No. Observations:                   42\n",
      "Model:                     ARMA(4, 1)   Log Likelihood                -376.584\n",
      "Method:                       css-mle   S.D. of innovations           1850.781\n",
      "Date:                Mon, 13 Apr 2020   AIC                            767.167\n",
      "Time:                        10:47:08   BIC                            779.331\n",
      "Sample:                    02-01-2000   HQIC                           771.626\n",
      "                         - 07-01-2003                                         \n",
      "===============================================================================\n",
      "                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "const          37.3039    129.751      0.288      0.775    -217.003     291.611\n",
      "ar.L1.Total    -0.8666      0.185     -4.692      0.000      -1.229      -0.505\n",
      "ar.L2.Total    -0.4236      0.166     -2.547      0.015      -0.750      -0.098\n",
      "ar.L3.Total    -0.5584      0.156     -3.579      0.001      -0.864      -0.253\n",
      "ar.L4.Total    -0.6144      0.126     -4.894      0.000      -0.861      -0.368\n",
      "ma.L1.Total     0.5197      0.219      2.370      0.023       0.090       0.950\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1            0.4929           -1.0592j            1.1683           -0.1807\n",
      "AR.2            0.4929           +1.0592j            1.1683            0.1807\n",
      "AR.3           -0.9473           -0.5431j            1.0920           -0.4171\n",
      "AR.4           -0.9473           +0.5431j            1.0920            0.4171\n",
      "MA.1           -1.9240           +0.0000j            1.9240            0.5000\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "#summary of the model\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## So the ARMA(4,1) model is:\n",
    "\n",
    "## $\\hat{y_t} = -0.87y_{t-1} - 0.42y_{t-2} - 0.56y_{t-3} - 0.61y_{t-4} + 0.52\\varepsilon_{t-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get prediction start and end dates\n",
    "pred_start_date = test_data.index[0]\n",
    "pred_end_date = test_data.index[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get the predictions and residuals\n",
    "predictions = model_fit.predict(start=pred_start_date, end=pred_end_date)\n",
    "residuals = test_data - predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1e8346fe588>"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(residuals)\n",
    "plt.title('Residuals from AR Model', fontsize=20)\n",
    "plt.ylabel('Error', fontsize=16)\n",
    "plt.axhline(0, color='r', linestyle='--', alpha=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Sales')"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "\n",
    "plt.plot(test_data)\n",
    "plt.plot(predictions)\n",
    "\n",
    "plt.legend(('Data', 'Predictions'), fontsize=16)\n",
    "\n",
    "plt.title('First Difference of Catfish Sales', fontsize=20)\n",
    "plt.ylabel('Sales', fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Squared Error: 2210.267116397745\n"
     ]
    }
   ],
   "source": [
    "print('Root Mean Squared Error:', np.sqrt(np.mean(residuals**2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
